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Shared Qs (trig_review)


  1. Question

    Consider a circle with a radius of length \(r=7.2\) meters. A central angle, in standard position, subtends an arc of length \(14.4\) meters.

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    Find \(\theta\) in radians.


    Solution


  2. Question

    Consider a circle with a radius of length \(r=9.6\) meters. A central angle, in standard position, subtends an arc of length \(45.6\) meters.

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    Find \(\theta\) in radians.


    Solution


  3. Question

    Consider a circle with a radius of length \(r=5.1\) meters. A central angle, in standard position, subtends an arc of length \(10.2\) meters.

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    Find \(\theta\) in radians.


    Solution


  4. Question

    Consider a circle with a radius of length \(r=6.9\) meters. A central angle, in standard position, subtends an arc of length \(13.8\) meters.

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    Find \(\theta\) in radians.


    Solution


  5. Question

    Consider a circle with a radius of length \(r=9\) meters. A central angle, in standard position, subtends an arc of length \(36.9\) meters.

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    Find \(\theta\) in radians.


    Solution


  6. Question

    Which graph shows an angle measuring \(\frac{4\pi}{9}\) radians in standard position?

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    1. A
    2. B
    3. C
    4. D
    5. E
    6. F
    7. G
    8. H

    Solution


  7. Question

    Which graph shows an angle measuring \(\frac{11\pi}{7}\) radians in standard position?

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    1. A
    2. B
    3. C
    4. D
    5. E
    6. F
    7. G
    8. H

    Solution


  8. Question

    Which graph shows an angle measuring \(\frac{10\pi}{11}\) radians in standard position?

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    1. A
    2. B
    3. C
    4. D
    5. E
    6. F
    7. G
    8. H

    Solution


  9. Question

    Which graph shows an angle measuring \(\frac{23\pi}{12}\) radians in standard position?

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    1. A
    2. B
    3. C
    4. D
    5. E
    6. F
    7. G
    8. H

    Solution


  10. Question

    Which graph shows an angle measuring \(\frac{\pi}{7}\) radians in standard position?

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    1. A
    2. B
    3. C
    4. D
    5. E
    6. F
    7. G
    8. H

    Solution


  11. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  12. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  13. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  14. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  15. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  16. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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  17. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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  18. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  19. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  20. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  21. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  22. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  23. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  24. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  25. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  26. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  27. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  28. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  29. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  30. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  31. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  32. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  33. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  34. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  35. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  36. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  37. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  38. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  39. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  40. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  41. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  42. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  43. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  44. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  45. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  46. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  47. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  48. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  49. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  50. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  51. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  52. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  53. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  54. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  55. Question

    Find the length or angle measure marked by \(x\). Please express your answer with 3 significant figures.

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    Solution


  56. Question

    An angle, \(\theta\), is shown below in standard position as a blue spiraling arrow. A radius (of length 1) is drawn at that angle. Where the radius connects to the circumference of the unit circle has Cartesian coordinates \((-0.761, 0.649)\).

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    Calculate the trigonometric ratios of \(\theta\).



    Solution


  57. Question

    An angle, \(\theta\), is shown below in standard position as a blue spiraling arrow. A radius (of length 1) is drawn at that angle. Where the radius connects to the circumference of the unit circle has Cartesian coordinates \((0.743, 0.669)\).

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    Calculate the trigonometric ratios of \(\theta\).



    Solution


  58. Question

    An angle, \(\theta\), is shown below in standard position as a blue spiraling arrow. A radius (of length 1) is drawn at that angle. Where the radius connects to the circumference of the unit circle has Cartesian coordinates \((0.468, 0.884)\).

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    Calculate the trigonometric ratios of \(\theta\).



    Solution


  59. Question

    An angle, \(\theta\), is shown below in standard position as a blue spiraling arrow. A radius (of length 1) is drawn at that angle. Where the radius connects to the circumference of the unit circle has Cartesian coordinates \((-0.556, -0.831)\).

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    Calculate the trigonometric ratios of \(\theta\).



    Solution


  60. Question

    An angle, \(\theta\), is shown below in standard position as a blue spiraling arrow. A radius (of length 1) is drawn at that angle. Where the radius connects to the circumference of the unit circle has Cartesian coordinates \((-0.822, 0.569)\).

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    Calculate the trigonometric ratios of \(\theta\).



    Solution


  61. Question

    Given:

    \[\cos(\theta)~=~-0.428\] \[\theta~\text{ is in quadrant III}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  62. Question

    Given:

    \[\cos(\theta)~=~-0.333\] \[\theta~\text{ is in quadrant II}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  63. Question

    Given:

    \[\cos(\theta)~=~-0.615\] \[\theta~\text{ is in quadrant III}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  64. Question

    Given:

    \[\cos(\theta)~=~0.801\] \[\theta~\text{ is in quadrant I}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  65. Question

    Given:

    \[\cos(\theta)~=~-0.168\] \[\theta~\text{ is in quadrant II}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  66. Question

    Given:

    \[\tan(\theta)~=~-3.8\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  67. Question

    Given:

    \[\tan(\theta)~=~2.5\] \[\theta~\text{ is in quadrant I}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  68. Question

    Given:

    \[\tan(\theta)~=~0.823\] \[\theta~\text{ is in quadrant III}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  69. Question

    Given:

    \[\tan(\theta)~=~-0.45\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  70. Question

    Given:

    \[\tan(\theta)~=~-0.196\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\sin(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  71. Question

    Given:

    \[\sin(\theta)~=~-0.241\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  72. Question

    Given:

    \[\sin(\theta)~=~-0.456\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  73. Question

    Given:

    \[\sin(\theta)~=~0.825\] \[\theta~\text{ is in quadrant I}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  74. Question

    Given:

    \[\sin(\theta)~=~0.636\] \[\theta~\text{ is in quadrant I}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  75. Question

    Given:

    \[\sin(\theta)~=~0.973\] \[\theta~\text{ is in quadrant I}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  76. Question

    Given:

    \[\tan(\theta)~=~1.82\] \[\theta~\text{ is in quadrant III}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  77. Question

    Given:

    \[\tan(\theta)~=~-3.13\] \[\theta~\text{ is in quadrant II}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  78. Question

    Given:

    \[\tan(\theta)~=~-1.17\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  79. Question

    Given:

    \[\tan(\theta)~=~-5.22\] \[\theta~\text{ is in quadrant II}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  80. Question

    Given:

    \[\tan(\theta)~=~-1.22\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\cos(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  81. Question

    Given:

    \[\sin(\theta)~=~0.987\] \[\theta~\text{ is in quadrant II}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  82. Question

    Given:

    \[\sin(\theta)~=~-0.27\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  83. Question

    Given:

    \[\sin(\theta)~=~0.468\] \[\theta~\text{ is in quadrant I}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  84. Question

    Given:

    \[\sin(\theta)~=~-0.547\] \[\theta~\text{ is in quadrant III}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  85. Question

    Given:

    \[\sin(\theta)~=~0.765\] \[\theta~\text{ is in quadrant II}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  86. Question

    Given:

    \[\cos(\theta)~=~0.48\] \[\theta~\text{ is in quadrant I}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  87. Question

    Given:

    \[\cos(\theta)~=~0.89\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  88. Question

    Given:

    \[\cos(\theta)~=~-0.872\] \[\theta~\text{ is in quadrant II}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  89. Question

    Given:

    \[\cos(\theta)~=~-0.874\] \[\theta~\text{ is in quadrant III}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  90. Question

    Given:

    \[\cos(\theta)~=~0.264\] \[\theta~\text{ is in quadrant IV}\]

    Find \(\tan(\theta)\). The tolerance is \(\pm 0.001\).


    Solution


  91. Question

    At noon, on an equinox, at the equator, the sun is directly overhead. Over land with minimal elevation change, we can approximate the local ground as flat.

    A rocket is launched at an angle of elevation of 0.643 radians above the horizon at a speed of 3630 meters per second.

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    How fast, in meters per second, is the shadow moving across the flat ground? The tolerance is \(\pm 10\) m/s.


    Solution


  92. Question

    At noon, on an equinox, at the equator, the sun is directly overhead. Over land with minimal elevation change, we can approximate the local ground as flat.

    A rocket is launched at an angle of elevation of 0.889 radians above the horizon at a speed of 2810 meters per second.

    plot of chunk unnamed-chunk-1

    How fast, in meters per second, is the shadow moving across the flat ground? The tolerance is \(\pm 10\) m/s.


    Solution


  93. Question

    At noon, on an equinox, at the equator, the sun is directly overhead. Over land with minimal elevation change, we can approximate the local ground as flat.

    A rocket is launched at an angle of elevation of 0.508 radians above the horizon at a speed of 3140 meters per second.

    plot of chunk unnamed-chunk-1

    How fast, in meters per second, is the shadow moving across the flat ground? The tolerance is \(\pm 10\) m/s.


    Solution


  94. Question

    At noon, on an equinox, at the equator, the sun is directly overhead. Over land with minimal elevation change, we can approximate the local ground as flat.

    A rocket is launched at an angle of elevation of 0.76 radians above the horizon at a speed of 4510 meters per second.

    plot of chunk unnamed-chunk-1

    How fast, in meters per second, is the shadow moving across the flat ground? The tolerance is \(\pm 10\) m/s.


    Solution


  95. Question

    At noon, on an equinox, at the equator, the sun is directly overhead. Over land with minimal elevation change, we can approximate the local ground as flat.

    A rocket is launched at an angle of elevation of 0.429 radians above the horizon at a speed of 4030 meters per second.

    plot of chunk unnamed-chunk-1

    How fast, in meters per second, is the shadow moving across the flat ground? The tolerance is \(\pm 10\) m/s.


    Solution


  96. Question

    At sunset, the sun’s rays are parallel to the local flat ground. A rocket is launched at an angle of elevation of 0.782 radians above the horizon at a speed of 4710 meters per second. Its shadow is projected onto a tall cliff to the east.

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    How fast, in meters per second, is the shadow moving up the cliff? The tolerance is \(\pm 10\) m/s.


    Solution


  97. Question

    At sunset, the sun’s rays are parallel to the local flat ground. A rocket is launched at an angle of elevation of 0.834 radians above the horizon at a speed of 2390 meters per second. Its shadow is projected onto a tall cliff to the east.

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    How fast, in meters per second, is the shadow moving up the cliff? The tolerance is \(\pm 10\) m/s.


    Solution


  98. Question

    At sunset, the sun’s rays are parallel to the local flat ground. A rocket is launched at an angle of elevation of 0.731 radians above the horizon at a speed of 2580 meters per second. Its shadow is projected onto a tall cliff to the east.

    plot of chunk unnamed-chunk-1

    How fast, in meters per second, is the shadow moving up the cliff? The tolerance is \(\pm 10\) m/s.


    Solution


  99. Question

    At sunset, the sun’s rays are parallel to the local flat ground. A rocket is launched at an angle of elevation of 0.724 radians above the horizon at a speed of 2680 meters per second. Its shadow is projected onto a tall cliff to the east.

    plot of chunk unnamed-chunk-1

    How fast, in meters per second, is the shadow moving up the cliff? The tolerance is \(\pm 10\) m/s.


    Solution


  100. Question

    At sunset, the sun’s rays are parallel to the local flat ground. A rocket is launched at an angle of elevation of 1.22 radians above the horizon at a speed of 3350 meters per second. Its shadow is projected onto a tall cliff to the east.

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    How fast, in meters per second, is the shadow moving up the cliff? The tolerance is \(\pm 10\) m/s.


    Solution


  101. Question

    A point on a Cartesian plane is given in polar coordinates: \[r = 5.07\] \[\theta=\frac{5\pi}{7}\]

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    Please determine the rectangular coordinates (\(x\) and \(y\)).



    Solution


  102. Question

    A point on a Cartesian plane is given in polar coordinates: \[r = 4.46\] \[\theta=\frac{4\pi}{5}\]

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    Please determine the rectangular coordinates (\(x\) and \(y\)).



    Solution


  103. Question

    A point on a Cartesian plane is given in polar coordinates: \[r = 3.75\] \[\theta=\frac{17\pi}{15}\]

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    Please determine the rectangular coordinates (\(x\) and \(y\)).



    Solution


  104. Question

    A point on a Cartesian plane is given in polar coordinates: \[r = 4.42\] \[\theta=\frac{9\pi}{5}\]

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    Please determine the rectangular coordinates (\(x\) and \(y\)).



    Solution


  105. Question

    A point on a Cartesian plane is given in polar coordinates: \[r = 3.61\] \[\theta=\frac{9\pi}{8}\]

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    Please determine the rectangular coordinates (\(x\) and \(y\)).



    Solution


  106. Question

    A point on a Cartesian plane is given in rectangular coordinates: \[x = -2.82\] \[y=3.13\]

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    Please determine the polar coordinates (\(r\) and \(\theta\)), enforcing \(0\le\theta<2\pi\).



    Solution


  107. Question

    A point on a Cartesian plane is given in rectangular coordinates: \[x = 3.52\] \[y=-1.85\]

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    Please determine the polar coordinates (\(r\) and \(\theta\)), enforcing \(0\le\theta<2\pi\).



    Solution


  108. Question

    A point on a Cartesian plane is given in rectangular coordinates: \[x = 2.6\] \[y=-2.18\]

    plot of chunk unnamed-chunk-2

    Please determine the polar coordinates (\(r\) and \(\theta\)), enforcing \(0\le\theta<2\pi\).



    Solution


  109. Question

    A point on a Cartesian plane is given in rectangular coordinates: \[x = -3.87\] \[y=-2.03\]

    plot of chunk unnamed-chunk-2

    Please determine the polar coordinates (\(r\) and \(\theta\)), enforcing \(0\le\theta<2\pi\).



    Solution


  110. Question

    A point on a Cartesian plane is given in rectangular coordinates: \[x = 2.61\] \[y=-3.78\]

    plot of chunk unnamed-chunk-2

    Please determine the polar coordinates (\(r\) and \(\theta\)), enforcing \(0\le\theta<2\pi\).



    Solution


  111. Question

    A canoe travels 2.3 m/s relative to the water. A river, heading east, flows at 3.5 m/s. The canoe points at a direction 1.43 radians counterclockwise from east.

    plot of chunk unnamed-chunk-1

    Find the canoe’s total speed, in m/s, and direction of travel, as radians counterclockwise from east. (In other words, find the canoe’s velocity relative to the ground, in polar form.)



    Solution


  112. Question

    A canoe travels 2.8 m/s relative to the water. A river, heading east, flows at 2.3 m/s. The canoe points at a direction 0.58 radians counterclockwise from east.

    plot of chunk unnamed-chunk-1

    Find the canoe’s total speed, in m/s, and direction of travel, as radians counterclockwise from east. (In other words, find the canoe’s velocity relative to the ground, in polar form.)



    Solution


  113. Question

    A canoe travels 3.3 m/s relative to the water. A river, heading east, flows at 2.0 m/s. The canoe points at a direction 0.89 radians counterclockwise from east.

    plot of chunk unnamed-chunk-1

    Find the canoe’s total speed, in m/s, and direction of travel, as radians counterclockwise from east. (In other words, find the canoe’s velocity relative to the ground, in polar form.)



    Solution


  114. Question

    A canoe travels 1.9 m/s relative to the water. A river, heading east, flows at 2.2 m/s. The canoe points at a direction 0.64 radians counterclockwise from east.

    plot of chunk unnamed-chunk-1

    Find the canoe’s total speed, in m/s, and direction of travel, as radians counterclockwise from east. (In other words, find the canoe’s velocity relative to the ground, in polar form.)



    Solution


  115. Question

    A canoe travels 1.7 m/s relative to the water. A river, heading east, flows at 2.8 m/s. The canoe points at a direction 2.08 radians counterclockwise from east.

    plot of chunk unnamed-chunk-1

    Find the canoe’s total speed, in m/s, and direction of travel, as radians counterclockwise from east. (In other words, find the canoe’s velocity relative to the ground, in polar form.)



    Solution


  116. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\sin\left(\pi\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  117. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\sin\left(\frac{7\pi}{6}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  118. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\sin\left(\frac{3\pi}{4}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  119. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\sin\left(\frac{5\pi}{3}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  120. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\sin\left(\frac{7\pi}{6}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  121. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\cos\left(2\pi\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  122. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\cos\left(\frac{5\pi}{3}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  123. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\cos\left(\frac{7\pi}{4}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  124. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\cos\left(0\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  125. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\cos\left(2\pi\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  126. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\tan\left(\frac{3\pi}{4}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  127. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\tan\left(\frac{\pi}{2}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  128. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\tan\left(\frac{5\pi}{6}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  129. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\tan\left(\frac{5\pi}{4}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution


  130. Question

    Use the unit circle to evaluate the trigonometric function at the indicated angle.

    \[\tan\left(\frac{2\pi}{3}\right)\]


    1. \(-\sqrt{3}\)
    2. \(-1\)
    3. \(\frac{-\sqrt{3}}{2}\)
    4. \(\frac{-\sqrt{2}}{2}\)
    5. \(\frac{-\sqrt{3}}{3}\)
    6. \(\frac{-1}{2}\)
    7. \(0\)
    8. \(\frac{1}{2}\)
    9. \(\frac{\sqrt{3}}{3}\)
    10. \(\frac{\sqrt{2}}{2}\)
    11. \(\frac{\sqrt{3}}{2}\)
    12. \(1\)
    13. \(\sqrt{3}\)
    14. \(\pm\infty\)

    Solution